From Morphology to Neural Information: The Electric Sense of the Skate

Marcelo Camperi1*, Timothy C. Tricas2,3, Brandon R. Brown1 1 Department of Physics, University of San Francisco, San Francisco, California, United States of America, 2 Department of Zoology, University of Hawaii at Manoa, Honolulu, Hawaii, United States of America, 3 Hawaii Institute of Marine Biology, University of Hawaii at Manoa, Honolulu, Hawaii, United States of America

Morphology typically enhances the fidelity of sensory systems. Sharks, skates, and rays have a well-developed electrosense that presents strikingly unique morphologies. Here, we model the dynamics of the peripheral electrosensory system of the skate, a dorsally flattened batoid, moving near an electric dipole source (e.g., a prey organism). We compute the coincident electric signals that develop across an array of the skate’s electrosensors, using electrodynamics married to precise morphological measurements of sensor location, infrastructure, and vector projection. Our results demonstrate that skate morphology enhances electrosensory information. Not only could the skate locate prey using a simple population vector algorithm, but its morphology also specifically leads to quick shifts in firing rates that are well-suited to the demonstrated bandwidth of the electrosensory system. Finally, we propose electrophysiology trials to test the modeling scheme.

Citation: Camperi M, Tricas TC, Brown BR (2007) From morphology to neural information: The electric sense of the skate. PLoS Comput Biol 3(6): e113. doi:10.1371/journal. pcbi.0030113

Introduction drop in apical-side potential with respect to the basal potential leads to an increased firing rate for the associated Sensor placement and arrangement are crucial for any nerves, while an increase in that potential difference leads to sensory system used to locate the distance and bearing of a an inhibited firing rate [11]. More recent measurements also stimulus source, and this is true for a variety of modalities. In delineate organ-specific and frequency-specific gain func- addition to stereo vision in much of the animal kingdom, tions [12,13]. The amplification mechanism of the sensory echolocation (e.g., the barn owl) and mechanosensory epithelium is not completely understood, but persuasive location (e.g., the sand scorpion) uses multiple sensors to models exist [11]. locate prey with requisite precision [1–3]. While previous studies have focused on the response Electrosensitive vertebrates, including monotremes (e.g., properties of single electroreceptors, few have explored the the platypus), siluriforms (e.g., the catfish), osteoglossomorphs simultaneous response of electroreceptor populations to (e.g., the knifefish), and chondrostreans (e.g., the sturgeon and biological stimuli. This aspect is especially relevant since the the paddlefish), typically possess large populations of in- pores and canals associated with the electroreceptors display dependent electrosensitive organs. Obviously, multiple or- great geometrical variation within a given organism and gans enhance signal-to-noise ratio by an increased number of among species [14]. In terms of higher processing, output simultaneous measurements since environmental electrical from principal cells in the dorsal octavolateralis nucleus signatures of biological relevance are often weak, even at (DON) of the skate hindbrain showed systematic responses to close range. However, these animals may also use the sensor oscillating dipole stimulation that were twice as strong as population to determine the location of electric sources. In responses to uniform body-wide fields [15]. Hence, it is the case of the black ghost knifefish, Apteronotus albifrons, the important to understand the coincident responses of the surface receptors simply report magnitudes of electric field, electrosensory periphery to electric stimuli to understand and the contrast of signal magnitudes across the body how central processing mechanisms integrate peripheral facilitate the location of nearby objects and the capture of receptor responses and affect behavior. prey [4,5]. Kalmijn has proposed an algorithm for elasmobranchs The elasmobranch fishes (sharks, skates, and rays) possess approaching stationary prey via the electric sense [16]. In an electrosensory system used to detect prey, possibly this model, the hunting elasmobranch simply maintains its navigate with respect to magnetic fields, and locate mates orientation with respect to the dipole field of the prey. [6–9]. The system includes hundreds or thousands of separate Geometrically, this means that the elasmobranch will always electrosensor units known as the ampullae of Lorenzini. The ampullae are often tightly clustered, but each is linked to an individual pore on the surface of the body via a long, gel-filled Editor: Karl J. Friston, University College London, United Kingdom canal (see Figure 1), and the pores are widely distributed (on Received February 12, 2007; Accepted May 4, 2007; Published June 15, 2007 the head and pectoral fins in skates and rays). Copyright: Ó 2007 Camperi et al. This is an open-access article distributed under Each ampulla is able to code minute electrical fluctuations the terms of the Creative Commons Attribution License, which permits unrestricted into discharge patterns of primary afferent nerves [10]. The use, distribution, and reproduction in any medium, provided the original author and source are credited. sensing cells of an ampulla’s epithelium detect electric potential differences between its apical side within the Abbreviations: DON, dorsal octavolateralis nucleus ampulla, and its basal side outside the ampulla. A sudden * To whom correspondence should be addressed. E-mail: [email protected]

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Author Summary

The electric sense appears in a variety of animals, from the shark to the platypus, and it facilitates short-range prey detection where environments limit sight. Typically, hundreds or thousands of sensors work in concert. In skates, rays, and sharks, each electro- sensor includes a small, innervated bulb, with a thin, gel-filled canal leading to a surface pore. While experiments have mapped single electrosensor activity, the mechanisms that integrate neural input from multiple electrosensors are still largely unknown. Here, we model the response of a precisely mapped subset of electrosensors responding in concert for a skate moving near stationary prey. Just as two ears help locate sound via time and intensity differences, we ask how a bilateral electrosensor array can contribute to electrical scene analysis. Our results show that the sensor array provides rich data for precise prey location, tuned by the morphology to render certain events, like the point of closest approach, ‘‘loud and clear.’’ This proof of principle makes a significant step in understanding the electric sense processing, and we recommend future experiments to compare and assess functions for the diversity of arrays found in other sharks and rays.

arrive at the source, even if this sometimes means an inefficient, spiraling path. In an initial simulation effort, one of us showed that the Kalmijn algorithm would typically mean that an elasmobranch moves in such a way to Figure 1. Simplified Schematic Depicting Two Ampullae within a Single reinforce the signal received by each electroreceptor [17]. Cluster, with Their Associated Canals and Pores However, recent behavioral analyses of sharks approaching Points A and C denote two pores, leading via gel-filled canals to their artificial electric dipoles show that the animals usually respective ampullae. Points B and D denote the inner ampullae, exhibit sharp turns toward the electric field source [18]. referencing electric potentials on the apical sides of the respective Thus, it appears that information regarding the source’s sensory epithelia. Point E is a common reference for the basal sides of ampullae within the cluster. The model used here emphasizes the location and/or the decision to approach the source is potential differences arising along the internal gel of the narrow canals developed rather quickly by the predator. These observa- as driving the apical potentials, which lead to excitation or inhibition tions are not necessarily at odds with the Kalmijn algorithm, based on their relation to the relatively constant basal potential at point E (see text). however. The algorithm could guide a creature for a brief doi:10.1371/journal.pcbi.0030113.g001 period of time until an overwhelming strength of signal among the sensor population helps it establish the exact location of the source. relevant morphological measurements and move beyond From the electrosensors, primary afferents project to electrical signals within the ampullae to the population principal cells of the DON in the medulla [19]. Ascending codes of neural information available to the elasmobranch efferent neurons in the skate have a strong ascending central nervous system. The canals in sharks’ electrosensory projection from the medulla to the contralateral midbrain, systems thoroughly map a 3-D space. While this is computa- where they converge in the lateral mesencephalic nucleus tionally straightforward, data representations and interpre- and the tectum, combining there with other sensory inputs tations are cumbersome. Therefore, we examine several [20]. Self-generated electrical signal subtraction has been scenarios for the peripheral electrosense of the dorso– convincingly documented in the elasmobranch DON [19,21]. ventrally flattened barndoor skate, Raja laevis, moving near While the afferent fibers show vigorous reactions to an an electric dipole. Adults are typically found at significant elasmobranch’s own ventilatory movements, the ascending benthic depths along mud floor troughs, where they skim efferent neurons demonstrate so-called common-mode suppression. In addition, electrical noise created by self- along the dark sea floor to feed on large crustaceans, generated movements may be cancelled by an adaptive filter mollusks, worms, and flatfish [23]. We model a barndoor via anti-Hebbian learning of ascending efferent neurons in skate moving near an electric dipole to represent the the hindbrain [22]. (By anti-Hebbian we mean responses to approach to a stationary prey, but these computations can familiar, repetitive stimuli are suppressed in favor of novel also represent a moving dipole source that approaches a stimuli.) However, how the combined neural responses from stationary skate. On average, the barndoor skate possesses a the periphery are processed by the DON, the midbrain, and greater number of electroreceptors than other skate species higher centers to determine prey headings is unexplored in [24]. The peripheral electrosensory geometry is precisely sharks and batoids. mapped [14], and it presents an almost perfectly 2-D system. Here, we model the system-wide signals and neural Where prior efforts stopped at voltage calculations [17], responses of an elasmobranch fish. In contrast to a prior here we take two further steps: we assess afferent spike modelingeffort[17],wenowuseprecise,biologically trains of the peripheral system, and present a basic model

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Figure 2. Canal Projections from the Dorsal Hyoid Ampullae of Raja laevis (A) Adapted from [14]. (B) As used in the present modeling work. Here, ampullary clusters are treated as a single point for simplicity. (B) also presents the canal numbering used in plots in this study. The 132 dorsal hyoid canals in the barndoor skate morphology are numbered consecutively, with canals 1 to 66 in the right cluster, and canals 67 to 132 in the left cluster. As seen in the figure, the first canal in each cluster is the one pointing in the most forward direction, 48 off the longitudinal axis. The other canals in each cluster are numbered consecutively, clockwise for the right cluster, and counterclockwise for the left cluster. Locations of pores and ampullae used in modeling match those in the actual fish (A). In terms of potential differences between an ampulla and a pore for a given canal (which is what our model emphasizes), the physics of electromagnetism tells us that the actual shape of the canals is immaterial. Thus, we simply represent them as straight lines. doi:10.1371/journal.pcbi.0030113.g002 that averages these afferent inputs to ascertain the location the rostral surfaces and the mandibular cluster on the jaw of a bioelectric field’s source. that presumably assists positioning for the final stages of feeding. Materials and Methods Though some authors have treated each canal as an equipotential or cable-like contact, linking the pore directly Computation of Signals to its associated ampulla [25–27], we agree with the viewpoint For the case of the skate moving with respect to a live that significant potential differences can and will develop source, we first compute the realistic voltage signals that within the length of the canals [28]. Here, consistent with an develop in the ampullae of Lorenzini using the skate’s earlier simulation [17], we emphasize the potential difference measured canal geometry. In this work, we concentrate on that develops between an electroreceptor and its associated the bilateral canals of the hyoid clusters that project to the pore, due to the electric field originating in the physical dorsal surface of the animal (see Figure 2). Of approximately electric dipole P of small bioelectric source (see Figure 3). 1,400 total ampullary canals in this species, we choose to The origin for our computations sits at the source electric focus on the dorsal hyoid cluster for two main reasons. First, dipole. The potential at all other points, referenced by the we narrow the focus for the sake of clarity and lucid data position vector r, is computed for an ideal electric dipole management; we show results for the signals arising from just 132 ampullae. Second, we choose the dorsal hyoid clusters [29], because they exhibit both the greatest canal lengths (corre- Q _ 1 P er sponding to the lowest signal thresholds; [12]) and also the V ¼ ð1Þ r 4pe r2 greatest variation of canal orientations when compared with other clusters. These clusters appear to be best suited for Here, P is the source’s dipole moment vector, which long-range detection when compared with the short canals of includes the orientation direction of the source; r is the

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contact between pores and ampullae [30]. The gel exhibits much stronger capacitive properties (charge storage) than seawater or generic collagen gels, suggesting a canal is better suited to sustaining electric potential differences than it is to bringing its two ends to quick electric equilibrium [30]. In fact, the relative electric resistance along either canal (e.g., from points A to B, or from points C to D; Figure 1) is more than 100 times greater than the electrical resistance between the pores A and C (in the semi-infinite seawater medium) [30]. Based on these measurements, and based on the observations of Murray regarding the crucial nature of geometric align- ment between the canal and applied electric fields [10], we believe that the potential differences evolving along canals will provide crucial voltages in the system, with a driving influence for the apical surface of the sensory epithelium. The electric potentials between nearby pores would approach the same electric potential before the electric potentials at either ends of a canal would equilibrate. Hence, as a skate draws close to an electric source, the sharply inhomogeneous source field will set up significant differences along the canals, depending on their length, angular orientation, and relative distance from the source [17]. Clustered ampullae will thereby be allowed to develop Figure 3. Skate Moving in a Source’s Frame of Reference distinct firing responses, as each develops distinct apical A point in the skate (a pore or an ampulla) is labeled by the vector r in the source’s reference frame. potentials. By treating the basal electric potential (VE,using doi:10.1371/journal.pcbi.0030113.g003 the geometry of Figure 1) as a constant for all ampullae in a given cluster, the model’s chief simplification is a focus on the voltages that arise along the interior length of the distance from the source to the point of interest; er is the unit canals. These lead to variations at the apical surface of the vector pointing from the source to the point of interest; and sensory epithelium, and with the basal potential treated as a e is the static permittivity of seawater (see Figure 3). Our constant, the apical variations drive the resulting firing entire computation is 2-D, approximating the dorso–ven- responses. trally flattened skate skimming the ocean floor in search of Our model treats the sensory epithelium as a ‘‘black box’’ prey. that translates transepithelial electrical fluctuations into As originally noted by Murray, maximum excitatory or firing rate alterations (see Analysis below). We do not imply inhibitory response occurs when an electric field vector is that it plays a minor role or that its electrical characteristics parallel or antiparallel to a canal [10]. This geometrical are trivial. The epithelium’s behavior is best described by observation is fundamental to our model, as this alignment multiple circuit elements acting in concert, with some maximizes the potential difference between a pore and its functioning as a strong impediment to current flow; as a associated ampulla. distinct electrical entity, its measured impedance exhibits We refer to the geometry of Figure 1 to describe our great variation, presumably resulting from the behavior and assumptions and computations of relevant potential differ- condition of epithelial ion channels [11]. These details are not ences in the electrosensory periphery. There are five geo- germane to our model, and we rely on the epithelium’s metric points of interest, labeled A through E. The two measured and predictable response to electrical stimuli. ampulla and respective canals belong to the same cluster At successive moments in time, as the skate moves with here. We assume that the basal voltage will be shared for each respect to the source dipole in close range (within 1 m of ampulla in a cluster (Figure 1, point E, within the sac that distance), we assign an electrical signal Vsignal to each surrounds the cluster). Far from a dipole or other electric electrosensor by computing the electric potential at the source, we assume all potentials at pores and ampullae to be various pores and associated ampullae, and then using the more or less equal, and the two organs will exhibit the same expression resting firing rate. Fluctuations in the ampulla relative to the V ¼ V V ð2Þ electric potential at point E will determine excited or signal ampulla pore inhibited firing rates for each organ. in which Vpore is the potential at the pore and Vampulla is the Since we treat the potential at Figure 1, point E, VE,asa potential in the internal ampulla chamber (apical side of the constant for all organs within a given cluster, the crucial sensing cells). For instance, using Figure 1, the electric signals quantities become the apical electric potentials within the are computed as the relative potential differences respectively ampullae (at points B and D in Figure 1). In what manner from points B to A and from points D to C. Here, both Vampulla would these electric potentials vary? Will they communicate and Vpore are computed using the classical expression for the electric potentials from their pores (Figure 1, points A and dipole electric potential. This is exactly equivalent to the path C)? Recent electrical measurements of the gel demonstrate integral treatment used in a previous effort [17]. Given the that the gel-filled canals do not provide good electrical simplifications described above, we do not pretend that our

PLoS Computational Biology | www.ploscompbiol.org1086 June 2007 | Volume 3 | Issue 6 | e113 Neural Information in the Electric Sense data will be the precise signals leading to firing alterations in These relaxations will be dominated by the rapidly develop- the skate—however, we believe our computations capture the ing electric potential changes over the short time scales of the dominant component of firing alterations that arise when the skate–dipole interaction (the most dramatic activity in the skate moves with respect to an electric field source. results that follow include 1–2 s of closest approach). As For the source dipole we use a magnitude that is consistent noted for weakly electric fish, electric perception is limited to with bioelectric fields measured for small prey, with dipole such short range that instantaneous data are presumably of values in the 10151016 Cm range [28]. While actual fundamental importance [31]. bioelectric fields do not conform exactly to an ideal dipole In addition to raw firing rate data, and to further explore field, using such fields makes for an excellent approximation the potential fates of firing rates entering the DON, we use for distances greater than the physical extent of the source the concept of firing-rate population vector, [32] which was itself. When comparing the ideal dipole field magnitude to used successfully in the prey location analysis for the sand the slightly more realistic physical dipole (separating the scorpion and the clawed frog [2,3]. positive and negative charge centers), we find that the ideal We use a basic form of a population vector, where its case gives values nearly identical to the physical dipole as long heading (or yaw) in the horizontal plane of the skate is as the skate-to-source separation is more than two to three determined by a weighted average of the headings of the times the size of the source. For instance, if the source were a various canals. The weighting of each canal orientation is bivalve with 3 cm separating its relatively positive and simply based on its electrosensor’s firing rate. We thus negative charge centers, the ideal dipole approximation consider a canal with heading h to correspond to a unit would be quite accurate as long as a skate was more than 6– vector (cos h, sin h) on the canal plane. We do this for both the 9 cm away. This approximation will be valid for the cases right and left canal clusters. The population vector (px,py)is explored here. then given by the weighted sum of individual unit vectors: In early simulations, one of us used a dipole moment 0 1 16 strength of 5.6 3 10 Cm [17]. This produced values for B C B X X C Vsignal in the range of tens to hundreds of nanovolts for the R;L 1 B C ðpx; pyÞ ¼ @ rðh; tÞcosðhÞ ; rðh; tÞsinðhÞA ð3Þ skate–source distances of interest. These low values con- NR;L RorL RorL gregate at the very center of the empirical gain function for canals canals computing afferent firing rates (see Analysis). In this region, the empirical fitting is most speculative. Therefore, we We take this vector to be a kind of compass heading that increased the dipole moment strength for the current can bias the animal’s orientation. In other words: simulations, using a value of 3 3 1015 Cm (i.e., around five py times the original choice). This is not far off from measured ðp ; p Þ¼pðcosh ; sinh Þ; h ¼ tan1 ; x y yaw yaw yaw p values for small prey sources [28], and renders values for qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x ð4Þ p ¼ p2 þ p2 Vsignal in the low microvolt range, where the translation to x y firing rate alterations is well mapped. While we cannot confirm that the DON actually computes Analysis such a population vector, it shows, at the very least, what We translate ampullary signals from Equation 2 into firing information is available to the skate from its peripheral rate alterations of the primary afferent neurons associated electrosense. with the ampullae. Again, treating the sensory epithelium as a ‘‘black box,’’ the Results firing process is modeled with an ad hoc firing rate gain function based on the known electrophysiology literature. To illustrate the first step of the calculations, we present an The model consists of a firing rate function ri(t) generated in a example ‘‘snapshot’’ of signal voltages for the skate near a given ampulla by the corresponding Vsignal. The index i refers source. Figure 5 displays potential differences developing to a specific ampulla–canal system, and t represents time. along the canals in Figure 2 for a skate approaching a source Firing rate functions ri(t) are obtained by multiplying the that is 30 cm to its left and 10 cm in front of it (as in Figure 3). indexed Vsignal values by a universal empirical gain function. Naturally, canals in the left hyoid ampullary cluster show the To build this gain function, we note that the resting tonic rate stronger signals. in the absence of electric fields is known to be in the range of We now present two example ‘‘swim-by’’ scenarios, with a 30 to 40 Hz [11]. Data from the thornback ray suggest 100% skate swimming in a straight path past a nearby source change in rate for each 5 lV of apical voltage fluctuation [19], (Figure 6). The responses presented here do not assess where negative drops are excitatory and positive fluctuations orientation behaviors; instead, they monitor the sensory are inhibitory, with a somewhat sigmoidal overall shape. information available to the skate as it moves past a While those points provide anchors for the ampullary gain bioelectric signal. function, the shape was derived by digitizing the experimen- In the first scenario, a skate swims at 0.5 m/s past a source tal points found in electrophysiology experiments with skates dipole with a closest approach distance of 0.15 m, in a [11], to which we applied the standard Levenberg-Marquardt direction parallel to the orientation of the source’s dipole. In algorithm for nonlinear fitting. The resulting canal gain the second scenario, a skate swims again at 0.5 m/s, but with a function can be seen in Figure 4. direction no longer parallel to the source’s dipole (458). For In this treatment, we factor neither the natural relaxation comparative purposes, the closest approach distance is again of voltage signals within the ampullary system nor the natural set to 0.15 m. relaxation of firing rate alteration in the primary afferents. As the skate moves in relation to the source in each of the

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Figure 4. Firing Rate Gain Function Used for Computing Neural Activity in the Primary Afferent Fibers Associated with the Ampullae

Available experimental data [11] was fitted to the sigmoid function 1.6 þ 62 / (1 þ 0.9 3 exp(Vsignal/11.5)). doi:10.1371/journal.pcbi.0030113.g004

two swim-by scenarios, the electric signal Vsignal associated dictated by the firing rate gain function of Figure 4, with with each electrosensory canal will change. Consequently, the the maximum change from the baseline firing occurring associated firing rates also become functions of time (i.e., a around the closest skate–source approach. function of environmental variables such as skate–source Analogous to the previous case, canals in the left cluster for distance and relative orientation). Figures 7 and 8 present scenario 2 are closer to the source during the entire swim-by, firing rate snapshots taken at different moments in each and their associated firing rates show the largest variations, as scenario. depicted in Figure 8. We again note that at skate–source As seen in Figure 6, canals in the right cluster for scenario 1 distances larger than 0.30 m, each firing rate is essentially at are closer to the source during the entire swim trajectory, and the baseline value. their associated firing rates show the largest variations, as To further explore how much neural information is depicted in Figure 7. Note that at skate–source distances available to the skate, we compute a firing rate population greater than 0.30 m, each firing rate is essentially at the vector for each dorsal hyoid ampullary cluster (Equation 3). baseline value of around 34 spikes/s. Figures 9 and 10 depict the resulting population vector As the separation distance decreases, the canals’ electric magnitudes versus time for each scenario, charting the 4 to 5 signals change in a nonuniform way. This leads to nonuni- s surrounding the point of closest approach. We depict the form firing rate profiles associated with each canal, as global or net population vector (i.e., summing for all hyoid

Figure 5. Relative Ampullary Electric Signal Snapshot for a Skate Approaching a Source that Is 30 cm to Its Left and 10 cm in Front of It Canal numbers correspond to those shown in Figure 1. doi:10.1371/journal.pcbi.0030113.g005

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Figure 6. Two ‘‘Swim-By’’ Scenarios Used in the Simulations doi:10.1371/journal.pcbi.0030113.g006 canals) as well as the bilateral left and right clusters the skate’s motion remained fixed in each of the swim-by individually. Inputs from left and right are not combined in scenarios, while the heading of the source would naturally the neural architecture until they reach the skate’s midbrain, vary given the skate’s motion. so the left and right vectors may be relevant to the DON (e.g., Figures 12 and 13 depict heading information from the processing common mode rejection). Also, note that the most global or net population vector. We plot the vector headings significant variations occur within a total time of approx- and the actual heading of the source dipole relative to the imately 1 s. skate over time during each encounter. Of note are the Like any vector, the population response includes angular abrupt discontinuities when the skate reaches the point of (or heading) information, which we relate to the actual closest approach to the source, and the near perfect match heading of the source (defined here as the angle between the (up to a constant phase) to the actual heading. In all of our skate’s direction of motion and the vector pointing to the simulations, population vector headings were defined with source position). Relevant angles are depicted in Figure 11. It respect to the skate’s longitudinal axis, following the usual is important to note that the dipole angle and the direction of counterclockwise mathematical convention. We note that

Figure 7. Firing Rate Snapshots, Representing the Instantaneous System Activity for Swim-By Scenario 1 Snapshots when skate–source distance was 0.50 m (A), 0.35 m (B), 0.25 m (C), the closest approach of 0.15 m (D), and 0.20 m after the closest approach (E). The abscissa refers to the canal numbers described in Figure 2. The ordinate refers to the firing rates associated with each ampulla. Dashed line indicates resting discharge rate. doi:10.1371/journal.pcbi.0030113.g007

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Figure 8. Firing Rate Snapshots, Representing the Instantaneous System Activity for Swim-By Scenario 2 Snapshots when skate–source distance was 0.50 m (A), 0.35 m (B), 0.25 m (C), the closest approach of 0.15 m (D), and 0.20 m after the closest approach (E). The abscissa refers to the canal numbers described in Figure 2. The ordinate refers to the firing rates associated with each ampulla. Dashed line indicates resting discharge rate. doi:10.1371/journal.pcbi.0030113.g008 such a human-centric system of angle definition need not from a model where pore potentials were communicated bear any relation to the skate’s neural processing of its directly to the apical side of sensing cells [25–27]. Slight electrical landscape. Hence, we believe constant offset phases rotations do not change pore magnitudes of electric potential (e.g., 908 alternately added to Figure 12 and subtracted from as appreciably as they change the canal potential differences Figure 13), can be considered without decreasing the considered in our model. predictive nature of the modeling data. In other words, we Another way to exhibit the spiking activity dependence on do not assert that the net population vector should act like an geometry is to plot the magnitude of the population vector orientation compass toward the dipole source. Rather, we for each canal cluster versus the external dipole angle (Figure point to relevant angular information encoded by the 16). Here, as in Figures 9 and 10, the population vectors for neuronal population’s spiking activity. both canal clusters have a magnitude of around 13.7 Hz when Finally, we suggest experimental tests of the model and its the source is far away or absent (i.e., Vsignal for each canal is assumptions. The following analysis can be tested directly by essentially zero). The maximum firing rate variation corre- benchtop electrophysiology measurements in which investi- sponds to an external dipole angle around 608 for the right gators use dipoles in various positions to map receptive fields cluster and 1208 for the left cluster. The opposing nature of in anesthetized skates (e.g., [15]). We note that existing data the geometric relationship between the skate and the dipole do not track dipole orientation. creates a predominance of positive electric potential signals, In this simulation, a dipole is placed near a stationary skate, which have an inhibitory effect on firing rates (see Figure 4). and the dipole is simply rotated in the horizontal plane of the A similar but excitatory result would be obtained if the skate without changing its position (Figure 14). This experi- external dipole were behind the skate, rather than in front of ment has not been conducted, to the best of our knowledge. it. By monitoring the resulting firing rate activity and computed population vectors, we can predict ‘‘sweet spots’’ or regions Discussion in which the electrosensory system of the skate should show specific and varied reactions to relatively small changes in Though bilaterally symmetric, the canal arrays are asym- dipole orientation. metric on either side as one moves from the anterior to Given the sharp dependence of our modeling system on the posterior regions of the skate. This has a dramatic effect on interplay of the canal geometry with the dipole field, a the encoding of neural data (e.g., Figure 5), and we wish to significant variation in neural response results. The firing rate emphasize two features in particular. First, the suppressed snapshots of Figure 15 show differences that arise in the and fairly uniform signals exhibited by ampullae in the right ampullae simply by changing the relative angle between the cluster (farther from the dipole) are dramatically different dipole and the skate. Such sharp contrast would not follow from those of the left cluster (closer to the dipole). This type

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Figure 9. Population Vector Magnitudes and Skate–Source Separation Distance (Top Panel) for Scenario 1 doi:10.1371/journal.pcbi.0030113.g009 of uniformity in the contralateral signals would not emerge if of signal polarity for the short groups of canals on each side the ampullae responded directly to pore potentials, and it that project medial on the body (canals 55–66 and 121–132 in does not emerge in data from a homogeneous array (see Figure 2). These subgroups effectively mimic the opposite Figures 17 and 18 below). Second, there is an abrupt reversal cluster; such a feature could presumably be of great use to the

Figure 10. Population Vector Magnitudes and Skate–Source Separation Distance (Top Panel) for Scenario 2 doi:10.1371/journal.pcbi.0030113.g010

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different cases. In the first, the source and the skate are aligned, and the source sits to the right of the skate’s path; in the second, the source and the skate are not aligned, and the source sits to the left of the skate’s path. While the skate clearly receives different information in these two scenarios, the global qualitative similarities of the firing rate snapshots for scenarios 1 and 2 overwhelm their differences. First we note that firing from ampullae on the side opposite of the source are nearly unaffected, even when the skate passes within 15 cm of the source. This corresponds to the left cluster in Figure 7 and right cluster in Figure 8, and is consistent with the relative potential data shown for the right cluster in Figure 5. Presumably, such consistent lack of excitation or inhibition would be very beneficial to the skate’s source location because it will provide a reference for contralateral excitation and inhibition by the source bio- Figure 11. Angular Measures in the Skate–Source Geometry electric field. Again, this is not the case for an artificial array To prevent multivaluedness issues, we define all angles in the usual of homogeneous canals. mathematical convention (i.e., 083608 range, counterclockwise with respect to the skate’s longitudinal axis). Next, we note the dramatic changes for steps D and E for doi:10.1371/journal.pcbi.0030113.g011 each trial. A sharp pattern of excitation and inhibition arises for the cluster nearest the source during the approach skate in common mode suppression or signal amplification at (Figures 7D and 8D). While some of the more anterior organs higher levels of neurosensory processing. (e.g., canals 1–15 in Figure 7) show firing excitations, For the firing rates computed, it is important to note that ampullae corresponding to the more posterior canals exhibit the variations revealed by our simulations are of significant nearly complete inhibition (e.g., canals 35–45 in Figure 7). magnitudes for even a simple neuronal system to respond As the skate passes and moves away from the source, accordingly. In a strict mathematical sense, this nonuniform consistent excitation emerges across the ipsilateral side. In firing rate profile encodes enough information for a precise particular, note that the organs experiencing inhibition on location of the source, although empirical neurophysiological approach shift abruptly to excitation. In Figure 7D and 7E, evidence is required to determine the processing of this for instance, organs 35–45 shift from near total inhibition to information by the skate central nervous system. near 100% excitation over a travel distance of only a few The two main swim-by scenarios present fundamentally centimeters by the skate. Not only would sharp changes

Figure 12. Net Population Vector Heading Data and Actual Source Heading versus Time for Scenario 1 The top graph depicts the separation distance over time. For this plot, a constant phase of 908 was added to the population vector data (see text). doi:10.1371/journal.pcbi.0030113.g012

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Figure 13. Net Population Vector Heading Data and Actual Source Heading versus Time for Scenario 2 The top graph depicts the separation distance over time. For this plot, a constant phase of 908 was subtracted from the population vector data (see text). doi:10.1371/journal.pcbi.0030113.g013

provide for simple interpretations, the rate of change demonstrated in these simple trials fits the response characteristics of the ampullae. Given the skate’s speed of 0.5 m/s, the organs in question experience this dramatic change over about 0.1 s, or at a frequency of 10 Hz. The time signature of this signal is within the ideal ampullary bandwidth of these organs [11,19]. And when considering the natural relaxation of firing rate alterations—afferent rates typically accommodate to a constant stimulus in less than 5 s [10]—the relatively quick changes shown in our trials again are within these neurophysiological constraints of the skate primary afferents. Both trials demonstrate asymmetry between approach and retreat situations, thus providing clear information concerning the anterior versus posterior source location. We note with interest that the largest excitations were observed for sources in anterior locations to the body and after the skate passed the dipole source. This observation is consistent with the functional subunit hypothesis [17], and indicates that the dorsal hyoid clusters may best detect and encode information concerning anterior bioelectric sources. As skates are not just predators but are also potential prey, our results suggest that these clusters may be used to detect the approach of a large predator or conspecific. The dorsal location adds weight to this speculation. In terms of electric source localization, the net population vector headings appear in Figures 12 and 13. Despite very different geometric scenarios in scenarios 1 and 2 (e.g., Figure 14. Geometric Arrangement for the Simulated Skate–Dipole opposite relative source-to-skate position and orientation), Benchtop Experiment the data relative to the actual source headings are virtually doi:10.1371/journal.pcbi.0030113.g014 identical. The population vector headings follow the change of

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Figure 15. Firing Rate Snapshots Representing the Instantaneous System Activity for the Simulated Benchtop Experiment of Figure 14 The external electric dipole angle is 08 (A), 458 (B), 908 (C), 1358 (D), and 1808 (E). The abscissa refers to the canal numbers described in Figure 2. The ordinate refers to the DON firing rates associated with each one of these canals. doi:10.1371/journal.pcbi.0030113.g015 the actual source headings with precision, with two notable The abrupt shift at the point of closest approach (at the 2-s deviations. First, the population vector headings do not mark) coincides with the magnitude of the net vector falling match the exact values of the source headings; second, an briefly to zero. (See solid lines for net vector magnitudes in abrupt shift of direction occurs at the point of nearest Figures 9 and 10.) We have confirmed that these shifts are approach. The fact that the precise angle values of the absolutely independent of our choice of reference frame— computed vectors do not match the apparent source headings the shifts are not an artifact of our angle definitions. As the is of very little concern, since we have imposed a human- skate moves from one side of the source dipole to the next, centric system of angle definition (e.g., Figure 11). Moreover, such a shift could be of significant biological benefit. The a skate could presumably compensate for such regular offsets, abrupt changes of vector magnitude and direction presum- much as visual processing inverts the actual image on the ably give the skate a very clear signal as it comes very close to retina. a prey, predator, or mate, and transitions from approach to moving away. In summary, the skate electrosensory array can provide a wealth of information on the heading of a nearby bioelectric source by using a simple population vector scheme. The morphology is well suited to tracking the source location, including information concerning whether the skate is moving toward or retreating from a source. In addition, population vector magnitudes vary sharply at the position of closest approach. This presumably supplies clear neural information that the source is within critical, minimum distance associated with the given swimming trajectory. Moreover, the changes in firing activity happen over a time scale that is ideally suited to the frequency response of the electrosensors. It is not unreasonable to suggest that the overall shape of R. laevis evolved at least in part for the tuning of electrosensory tasks, especially as the dorsal hyoid canal pores extend to the periphery of the skate’s wings (Figure 2). The location of the Figure 16. Population Vector Magnitude as a Function of the External hyoid pores follows this pattern for the canal systems of most Dipole Angle, as Defined in Figure 14 skates [24]. The ‘‘baseline’’ curve represents the magnitude of the population vector in the absence of an electric dipole field. Does the skate morphology confer an obvious advantage doi:10.1371/journal.pcbi.0030113.g016 over, for instance, a simple homogeneous array of canals? We

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naturally, of much greater range, reflecting the range of canal lengths—the signals of the skate’s system are three times that of what a homogeneous array would offer. Even if one adjusts the canal lengths of this artificial array to the maximum skate canal length, however, a more fundamental difference remains. The canal-to-canal signal differences vary in a moderate fashion for the artificial array, while those in the skate vary dramatically, even for some nearly adjacent canals. Figure 5 exhibits signals that change by approximately 50% over as few as three canal spacings, while Figure 18 shows that a similarly dramatic difference can only be obtained over 15– 20 canal spacings. Further computations of firing profiles and population vector magnitudes exhibit the same fundamental differences shown in Figure 18. The size of signals are typically smaller for the artificial canal array, and in all cases the signals change more gradually, as shown both over the array of canals, and also over time, in the case of the population vector magnitudes. These trials confirm that a homogeneous array can also track the source dipole, but at least two distinct advantages for the skate’s varied canal morphology emerge. First, the Figure 17. An Artificial Array of Canals for a Hypothetical Dorsal Hyoid ‘‘snapshot’’ canal voltages (see Figure 5 and Figure 18) are Cluster much less dramatic for the artificial array; the contralateral doi:10.1371/journal.pcbi.0030113.g017 cluster does not exhibit a homogenous set of voltages, and the variation of signals within the near-side cluster exhibits a ran the same simulations for an artificial set of dorsal hyoid much less pronounced change. In essence, the homogeneous, electrosensors with associated canals of uniform 10-cm artificial array would not provide the same sharp contrast of lengths and equal angular spacing covering 3608 of horizontal signals between organs. Second, though firing rates and arc. population vectors change for the artificial array, they change Figure 17 depicts a homogeneous array of 132 canals, with more slowly over time. As noted previously, referencing 66 per cluster, as in the skate (compare with Figure 2). The Figure 7, a subset of canals can change their firing rate from two clusters have the same lateral spacing as those in the near 0 to 50 Hz over about 0.1 s as the skate moves past the skate. The canal lengths of the artificial array are set to 10 cm, dipole. Similarly, the skate’s morphology provides population the average length of those for the skate’s dorsal hyoid vector magnitudes that nearly double in less than 0.25 s, while cluster; the angular distribution is similarly uniform, with a similar change in the artificial array takes a second or more. canals placed every 2.788, as opposed to the skate’s actual This is crucial when one considers that the electrosensory canals, which have some densely spaced canals in terms of system of the skate is finely tuned to changes in a narrow orientation, while some others are spaced more broadly. bandwidth peaked between 2 and 10 Hz [10–12,19]. Hence, an We compute a snapshot of Vsignal, according to Equation 2, abrupt change evolving in a fraction of a second would be for each of the canals, exactly as we did for the skate array. much more useful than a change that takes a second or more. The results are shown in Figure 18 (compare with Figure 5). To correctly model the function of the electrosensory The significant differences for the skate versus the homoge- periphery, it is critical to understand the excitation of canal neous, artificial array are as follows. The skate signals are, arrays by bioelectric fields. We have proposed a simple,

Figure 18. Relative Ampullary Electric Signal Snapshot for the Artificial Array Approaching a Source that is 30 cm to Its Left and 10 cm in Front of It doi:10.1371/journal.pcbi.0030113.g018

PLoS Computational Biology | www.ploscompbiol.org1095 June 2007 | Volume 3 | Issue 6 | e113 Neural Information in the Electric Sense specific test for the modeling scheme advocated here. We the ventral surface. These canals are more continuous in identify an area of specific opposite predictions from our distribution, and have prominent contralateral projections model and that of cable-like, equipotential canal function. As thatcoverawiderangularfield.Evenmoredramatic the dipole of Figure 14 turns between 08–908, the anterior differences in canal projection vectors exist among the dorsal pore potentials (e.g., for canals 0–50 in the left cluster) and ventral buccal clusters. Application of the electro- become increasingly positive, via the dot product of Equation dynamic model that integrates responses of these ampullary 1. Hence, a cable-like canal function, conveying the pore groups would provide a more comprehensive model of potential to the ampullae, would predict inhibited firing rates electrosensory processing of environmental fields in feeding, for increasing apical potentials. However, our model predicts social behavior, and navigation. In addition, it would permit the opposite, as can be seen in Figure 15A–15C. The turn development of models for testing the functional subunit between 08 and 908 yields negative V values and excited signal hypothesis [14], in which information from subgroups of firing rates. Furthermore, according to the data shown in canals in different clusters that have similar directional Figures 15 and 16, a quick dipole rotation from just 08 to 458 projections may be integrated to maximize direction compu- would appreciably alter not only the firing rates associated tations. with the anterior canals but also the population vector magnitudes. These changes could be exhibited in primary Future comparative work that assesses electrosensory- afferent rates, ventilatory activity, heart rate, or even DON processing mechanisms across taxa will also provide impor- activity. A traditional theory by which canals simply convey tant clues on the evolution and diversity of ampullary arrays pore voltage signals to the ampullae would not be as sensitive seen in elasmobranch fishes. to the canal’s overall alignment with the dipole field vectors. We have modeled the neural responses of only a small Acknowledgments subset of the approximately 1,400 ampullary canals in the The authors thank Ariel Rivera and Leo van Hemmen for discussions barndoor skate. While we chose the approximately 132 hyoid of the model. We are also grateful to the anonymous reviewers for canals that project to the dorsal surface of the skate’s body for insightful comments and suggestions. their apparent sensitivity and to present clear and finite data, Author contributions. BRB and TCT conceived the experiments, future efforts incorporating all clusters are required to and MC and BRB designed the experiments. MC performed the understand central processing and integration of receptor experiments. BRB, MC, and TCT analyzed the data. MC and TCT contributed reagents/materials/analysis tools. BRB, MC, and TCT population data. Even more dramatic and discontinuous wrote the paper. rostral and caudal projections are found in the dorsal canals Funding. The authors received no specific funding for this study. of the skate superficial ophthalmic cluster [14]. In addition, Competing interests. The authors have declared that no competing there are approximately 700 total hyoid canals that project to interests exist.

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